Methods for processing dispersive acoustic waveforms

ABSTRACT

A method for processing acoustic data comprising applying a dynamic filter band. The method and apparatus may be particularly adapted to processing sonic data to measure formation slowness in a borehole.

FIELD OF THE INVENTION

The present invention relates generally to methods and apparatus fordetecting, removing and/or isolating signals from acoustic waveformdata. More particularly, it relates to methods for processing dataacquired from sonic borehole logging.

BACKGROUND OF THE INVENTION

Acoustic tools are useful in providing a large range of informationregarding formation and borehole parameters adjacent the tools. Aprimary use of acoustic borehole measurements is for estimatingcompressional and/or shear wave formation slowness. Formation slownessis not measured directly but rather is determined from the variousacoustic waveforms received by the receivers. Formation slowness isoften measured by placing an array of sensors in a sonde in a borehole,the array including at least one transmitter and at least one receiver;transmitting an acoustic signal from the transmitter; receiving theacoustic signal with the receiver; and calculating the formationslowness considering the distance between the transmitter and receiverand the time between transmission of the signal by the transmitter andsignal receipt at the receiver. Calculating the formation slowness iscomplex however as many different acoustic types of signals are receivedin response to a transmitted signal. A single transmitted acousticsignal, whether monopole, dipole, quadrapole, or multipole, can generatea variety of waves in a borehole environment that are received by thereceivers. To process the acoustic data, it is necessary to separate andclassify the various received waves into general waveform categoriessuch as compressional, shear and Stoneley arrivals.

One method to estimate formation slowness is the slowness-time coherence(STC) method wherein the semblance peaks of the waveforms received bythe sensor array are located in a slowness-time plane. U.S. Pat. No.4,594,691 describes STC processing and is incorporated herein in itsentirety. Certain received signals, such as those generated by thedipole flexural mode, are dispersive. For dispersive modes, a dispersivevariation of STC processing, such as Dispersive STC (DSTC) processing asdescribed in U.S. Pat. No. 5,278,805 and QDSTC as described in U.S. Pat.No. 5,587,966, each of which are incorporated herein in their entirety;is useful when processing dispersive acoustic data. One particular useof STC processing is to determine the compressional and shear slownessof the formation.

STC semblance processing facilitates the determination of slowness forvarious components propagating across an array of sonic waveforms. Theresult of semblance processing is normally represented in atwo-dimensional time-slowness map (time vs. slowness). The result ofsemblance processing is normally presented versus depth by projectingthe time-slowness map onto the slowness axis according to the followingequation: ${P_{i}(s)} = {\max\limits_{t}{\rho_{i}\left( {S,t} \right)}}$

-   -   where P_(i) is the slowness projection, and        -   ρ_(i) is the semblance computed at each level, which is a            function of the slowness, S, and time, t.

In STC processing, a window or band in the slowness-time plane isidentified with each type of arrival. In order to minimize the effect ofparameter uncertainty in dispersive STC, the processing band isdynamically adjusted depending on the stacking slowness and the measuredborehole diameter, taking the sensitivity to these parameters intoaccount. Although robust and useful, DSTC processing has limitations.Basic assumptions in DSTC processing are that borehole formations arehomogeneous, isotropic formations and that the tool effects in thereceived signals owing to the presence of the tool in the borehole canbe easily addressed. As advances are made in borehole acoustic tools andprocessing of sonic logging data, these assumptions may be revisited.

In dipole sonic logging, a flexural wave moves through the boreholefluid and along the borehole wall at a rate dependent upon the velocityof the borehole fluid (i.e. mud slowness) and the shear slowness of theformation. The flexural mode is also sensitive to other parameters suchas borehole diameter, densities and compressional slowness of theformation. These parameters need to be considered but their exact valuesmay be difficult to determine. The lack of precise values for theparameters means that the final slowness estimation will also includesome degree of uncertainty. Furthermore, these can vary throughout theborehole logging, making it inaccurate to apply a uniform value orcorrection throughout a logged interval.

In evaluating sonic data, it would be useful to provide a measure of thedegree of uncertainty in the final slowness estimation. The presentinvention is directed toward a method of determining dispersion factorsin dipole sonic logging and the sensitivity of the calculated formationshear slowness to such factors. In particular, the present inventionprovides methods to determine the sensitivity of the flexural modeslowness to the formation shear slowness in dipole acoustic logging.

Additional advantages and novel features of the invention will be setforth in the description which follows or may be learned by thoseskilled in the art through reading these materials or practicing theinvention. The advantages of the invention may be achieved through themeans recited in the attached claims.

SUMMARY OF THE INVENTION

The present invention provides methods to minimize the possibility oferror in acoustic data caused by the presence of the tool in theborehole and other uncertainties in the model parameters. The presentinvention provides a method for processing acoustic data using DSTCprocessing that comprises calculating dispersion sensitivity andimplementing a dynamic processing frequency band to minimize the effectsof model error. The method further comprises determining sensitivitylimits or “cut-offs” in the received acoustic data for variousparameters, including tool presence in the borehole. One such limit onthe useful frequency band for processing is established by therealization that the sensitivity of the flexural mode arrivals dependson the frequency of the transmitted signal. Another embodiment of thepresent invention comprises an iterative process at each depth levelwherein a first slowness is estimated using parameters assuming ahomogenous isotropic model, and then semblance processing is iterativelyrepeated until a stop criteria is satisfied. Examples of stop criteriainclude a decreased error bar size, a minimized change in slownessbetween iterations, or a coherence (mean or peak) that decreases below athreshold.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings illustrate preferred embodiments of thepresent invention and are a part of the specification. Together with thefollowing description, the drawings demonstrate and explain theprinciples of the present invention.

FIG. 1 shows a schematic of a conventional acoustic tool disposed in aborehole;

FIGS. 2A and 2B show the sensitivity of the flexural mode slowness tothe various parameters in a fast formation;

FIGS. 3A and 3B show the sensitivity of the flexural mode slowness tothe various parameters in a slow formation (e.g. Ss=600 μs/ft);

FIG. 4A displays model results for configurations in a six-inch boreholewith the tool in the borehole and results for borehole configurationswith fluid only in the boreholes for various combinations of signalfrequency and calculated slowness;

FIG. 4B shows the difference in slowness between tool-included andtool-absent models across the frequency range from 0 to 8 kHz as modeledin a six-inch borehole;

FIG. 5A displays model results for configurations in a twelve-inchborehole with the tool in the borehole and results for configurationswith fluid only in the boreholes for various combinations of signalfrequency and calculated slowness;

FIG. 5B shows the difference in slowness between tool-included andtool-absent models across the frequency range from 0 to 8 kHz as modeledin a six-inch borehole;

FIG. 6 shows a residual difference value minimized in order to permit anequivalent borehole diameter to be defined;

FIG. 7 shows a set of tables of offsets a(S,d) for different fluidslownesses; and

FIG. 8 shows that the dynamic filter band varies with depth, and dependson the equivalent borehole diameter, and the stacking slowness.

DETAILED DESCRIPTION

Turning now to the figures, and in particular to FIG. 1, an acoustictool (100) is shown adjacent to a homogeneous formation (102). Thehomogeneous formation (102) is cased with a casing (104). The acoustictool (100) includes at least 3 transducers consisting of at least onetransmitter (T), and at least one receiver (R). In the presentembodiment there are two receivers (R) and one transmitter (T), however,many more receivers (R) and transmitters (T) may also be used. The onetransmitter (T), two receiver (R) arrangement shown is exemplary innature and there may be a full array of receivers and/or transmitters,or a single transmitter (T) and receiver (R). The receivers (R) andtransmitter (T) are coupled to a computer processor (106) for collectingand processing data from the acoustic tool (100). Also shown is a waveray path (108) representing a path for a compressional wave caused byactivation of the transmitter (T). The receivers (R) may be of differenttypes, including, but not limited to, piezoelectric and magnetostrictivereceivers. The receivers (R) are able to detect the arrival of sonicwaves.

Information or data collected from the acoustic tool (100), which mayinclude waveforms generated by the receivers (R) over time, is sent tothe computer processor (106) via a cable (110) from which the acoustictool (100) is suspended. Data may also be sent between the computerprocessor (106) and the receivers (R) by any other convenientcommunication technique. The computer processor (106) is commerciallyavailable from a wide variety of sources. The acoustic data taken by theacoustic tool (100) and received by the computer processor (106) may beprocessed according to STC processing.

In one embodiment, the method of the present invention comprisesgenerating a set of estimated slowness curves. Slowness calculations aresensitive to a variety of borehole parameters, including parameters suchas borehole diameter, fluid slowness, density and the ratio ofcompressional slowness (Vp) to shear slowness (Vs). In order to evaluatethe error in the slowness estimation, the sensitivity of the dispersionto the various parameters is computed. The sensitivity of the flexuralmode dispersion in the fluid-filled borehole may be estimated asfollows: LetP={P ₁ , P ₂ , P ₃ , P ₄ , P ₅ }={S _(s) ,V _(p) /Vs,HD,S _(mud),DR}  (1)The relative sensitivity of the flexural mode slowness, s_(k)(P₀,f), tothe parameter, P_(k), at frequency, f, was defined as: $\begin{matrix}{{s_{k}\left( {P_{0},f} \right)} = {{\frac{P_{k}}{S_{flex}\left( {P,f} \right)}\frac{\partial{S_{flex}\left( {P,f} \right)}}{\partial P_{k}}}❘_{P = P_{0}}}} & (2)\end{matrix}$where S_(flex)(P,f) is the phase slowness of the flexural wave for theparameter P at frequency f; S_(s) is the formation shear slowness; Vp/Vsis the ratio of compressional and shear wave speed; HD is the boreholediameter; S_(mud) is the fluid slowness and DR is the ratio of theformation and fluid densities.

FIGS. 2A and 2B show the sensitivity of the flexural mode slowness tothe various parameters in a fast formation. As seen in FIGS. 2A and 2B,the sensitivity of the flexural mode slowness to the formation shearslowness in a fast formation drops out at a certain frequency and thesensitivity to other parameters, especially borehole diameter and fluidslowness, becomes dominant. For example, in the fast formation (Ss=100μs/ft), the sensitivity to the shear slowness drops rapidly at 4 kHz forthe 6-inch borehole (FIG. 2A) and at 2.5 kHz (FIG. 2B) for the 12-inch.Conversely, the sensitivity to the borehole diameter and mud slownessgrows rapidly at these frequencies. Therefore, it is desirable that theprocessing frequency band be below this frequency to filter out thesesensitivity effects.

FIGS. 3A and 3B shows the sensitivity of the flexural mode slowness tothe various parameters in a slow formation (e.g. Ss=600 μs/ft). As seenin FIGS. 3A and 3B, the sensitivity of the flexural mode slowness to theformation shear slowness does not change as much as it does for fastformation. Also, the sensitivity to the other parameters is relativelylow. Thus in slow formations, the entire frequency component may beutilized to get the highest possible signal level.

Slowness calculations also may be sensitive to the presence of the toolin borehole. Another embodiment of the present invention comprises amethod of determining formation slowness, the method considering theeffect of the tool presence in a borehole, by modeling a borehole toolstructure and a fluid-filled borehole by equivalent coaxial materialsand searches for the various arrival modes. FIG. 4A displays modelresults for configurations in a six-inch borehole with the tool in theborehole and results for borehole configurations with fluid only in theboreholes for various combinations of signal frequency and calculatedslowness. FIG. 4B shows the difference in slowness between tool-includedand tool-absent models across the frequency range from 0 to 8 kHz asmodeled in a six-inch borehole. FIG. 5A displays model results forconfigurations in a twelve-inch borehole with the tool in the boreholeand results for configurations with fluid only in the boreholes forvarious combinations of signal frequency and calculated slowness. FIG.5B shows the difference in slowness between tool-included andtool-absent models across the frequency range from 0 to 8 kHz as modeledin a six-inch borehole.

It is noted that, in general, the difference in the frequency band wherethe sensitivity to the formation shear slowness is unity is very smallor negligible. The sensitivity cut-off in the fast formation (Ss=100μs/ft), small borehole (HD=6 in.), is about 4 KHz (FIG. 2A) and thedifference in dispersion curves is less than 1% up to this frequency(FIG. 4A). The difference in dispersion curve in the large borehole(HD=12 in.) is again less than 1% up to 2.3 KHz (FIG. 5). Note that thesensitivity cut-off frequency depends on the tool structure, boreholediameter and formation shear slowness (FIG. 2, 3). Therefore, carefulselection of the processing frequency band is essential in order tomaintain the validity of this observation. Also note that the effect ofthe tool presence depends on both the borehole diameter and theformation slowness (FIGS. 4, 5).

The difference in dispersion curves due to the tool presence is about 1%up to 3 KHz, which covers most of the signal, and the sensitivity to theborehole diameter is relatively low in the 6-in. borehole (FIG. 4) andis always less than 1% in the borehole larger than 12 in. (FIG. 5).Compared to the dispersion curve for the borehole with no tool present,the dispersion curve when the tool structure is present is shiftedslightly to the lower frequency and almost equivalent to the slightlylarger borehole.

In some embodiments of the present invention, the frequency selection isperformed dynamically using automatic and adaptive frequency filter bandselection. Because the sensitivity cut-off frequency with the toolpresent is the focus of interest, the relationship between dispersioncurves with and without tool presence will be derived. In order toobtain this relationship, the residual difference, R, of the twodispersion curves is defined as: $\begin{matrix}{R = {\sum\limits_{f}{{{S_{S_{s}}\left( {S,f} \right)}\left\{ {{S_{tool}\left( {S,f,d} \right)} - {S_{empty}\left( {S,f,{d + {a\left( {S,d} \right)}}} \right)}} \right\}}}^{2}}} & (3)\end{matrix}$where S is formation shear slowness, S_(Ss), is the sensitivity to theformation shear slowness, S_(tool) is the dispersion curve with the toolpresent and S_(empty) is the dispersion curve without the presence ofthe tool, d is the borehole diameter, and f is the frequency. R is thenminimized for a, for each S and d (FIG. 6), thereby permitting anequivalent borehole diameter to be defined as d+a(S,d) wherein a(S,d) isthe offset. A set of tables of offsets a(S,d) (FIG. 7) for differentfluid slownesses may be computed and is included in the DSTC.

Using the generated set of dispersion curves computed for givenparameters, (Vp, fluid slowness and density), it is possible todetermine the expected uncertainty in shear slowness estimation, e, dueto the expected uncertainty in the borehole diameter measurement,δ_(hd), by taking the ratio of sensitivity to the borehole diameter,s_(hd), and the sensitivity to the formation shear slowness, s_(shear).$\begin{matrix}{{{e\left( {S,f} \right)} = {\frac{s_{hd}\left( {S,f} \right)}{s_{shear}\left( {S,f} \right)}\delta_{hd}}},} & (4)\end{matrix}$The equivalent borehole diameter may then be used to determine thefrequency upper limit and the expected uncertainty in shear slownessestimation, e, the processing upper limit f_(a) (S) may be defined as afrequency f_(u) where the integral of e(S,f) from 0 to f_(u) reaches apredefined threshold, E, for each slowness, S. $\begin{matrix}{{E \geq {\int_{0}^{f_{u}}{{e\left( {S,f} \right)}{\mathbb{d}f}}}},} & (5)\end{matrix}$E and δ_(hd) are may be set to initial values, for example, 25 and 0.1respectively. Optimal value for E and δ_(hd) may be determined fromexperimental data. In order to consider the effect of the presence of atool, according to one embodiment of the invention, an offset a(S,d) maybe added to the borehole diameter, such that the upper frequency may becalculated as:f _(upper)=(s,d)(a(S,d)+d)/d,  (6)alternatively, the following expression could also be used:f _(upper) =f(S, d _(—) e),  (7)where d_e is the equivalent borehole diameter.In some embodiments, the processing frequency lower limit may becalculated to have a constant factor defined as: $\begin{matrix}{q = {\frac{1}{2}\frac{\left( {f_{upper} + f_{lower}} \right)}{\left( {f_{upper} - f_{lower}} \right)}}} & (8)\end{matrix}$wherein q is fixed initially at 1.0 and the center frequency is the Airyphase frequency, numerically calculated as the frequency where dk/dω) ofthe mode has a maximum value.

In some embodiments, the waveforms may be dynamically filtered beforethe back propagation and stacking in the DSTC processing. The dynamicfilter band varies with depth, and depends on the equivalent boreholediameter, d, and the stacking slowness, S (FIG. 8). The presentinvention comprises a modified DSTC process comprising computing thesemblance p(S, τ) as follows: $\begin{matrix}{{{{Let}\quad{{Xk}(f)}} = {F\left\{ {{xk}(t)} \right\}}},{{\rho\left( {S,\tau} \right)} = \frac{\sum\limits_{t = {\tau - T}}^{\tau}{{\sum\limits_{k = 1}^{M}{F^{- 1}\left\{ {{W\left( {f,S,d} \right)}{X_{k}(f)}{\mathbb{e}}^{{- 2}{\pi f\mathbb{i}r}_{k}{\alpha{({f,S,d})}}}} \right\}}}}^{2}}{\sum\limits_{t = {\upsilon - T}}^{T}{\sum\limits_{k = 1}^{M}{{F^{- 1}\left\{ {{W\left( {f,S,d} \right)}{X_{k}(f)}{\mathbb{e}}^{{- 2}{\pi f\mathbb{i}r}_{k}{\alpha{({f,S,d})}}}} \right\}}}^{2}}}}} & (9)\end{matrix}$where xk(t) is the signal of the k^(th) receiver, t is the sample time,f is the frequency, F { } is the Fourier transform, F-1 { } is theinverse Fourier transform, S is the formation shear slowness (parameterto be estimated), d is the borehole diameter, τ is the position ofintegration time window, W(f, S, d) is the filter response whose cut-offfrequencies are dynamically computed depending on the formation shearslowness S and borehole diameter d, α(f, S, d) is theoretical phasedelay per unit length at frequency f, i is the square root of (−1),r_(k) is the distance between the k_(th) receiver and the stackingreference point, M is the number of receivers and T is the length of thetime window in which the semblance is calculated. The overall data flowmay be as shown in FIG. 9. Note that the mode search is performed toproduce a set of reference dispersion curves for each stacking slownessand the back-propagator is generated for each stacking slowness and foreach receiver. The optimal processing band is then calculated and thefilters are designed for each stacking slowness. The filter coefficientsare multiplied to the back-propagator so that the back-propagatedwaveform is automatically filtered to have the optimum frequency band.

In some embodiments the inverse Fourier transform takes only thepositive frequency part into account so that the results become complexanalytic signals and their norm are the envelopes of the stackedfrequency.

The present method of processing of acoustic data automatically adjuststhe processing frequency band to reject the model error, including thetool effect. An equivalent borehole diameter was introduced toapproximate the dispersion curve with the tool effect by scaling thedispersion curve without tool effect. The processing uses the equivalentborehole diameter via a pre-computed table of the scale factors. Thedescription and figures above present a methodology and apparatus fordynamically filtering acoustic waveforms.

The preceding description has been presented only to illustrate anddescribe the invention. It is not intended to be exhaustive or to limitthe invention to any precise form disclosed. Many modifications andvariations are possible in light of the above teaching. The preferredembodiment was chosen and described in order to best explain theprinciples of the invention and its practical application. The precedingdescription is intended to enable others skilled in the art to bestutilize the invention in various embodiments and with variousmodifications as are suited to the particular use contemplated. It isintended that the scope of the invention be defined by the followingclaims.

1. A method of processing acoustic data comprising: generating a set ofestimated slowness curves; determining uncertainty in the estimatedslowness curves; determining an upper limit for a frequency filter band;determining a lower frequency limit for the frequency filter band; andapplying the frequency filter band in calculating semblance.
 2. Themethod of claim 1, wherein the step of generating a set of curvescomprises determining a sensitivity cut-off frequency.
 3. The method ofclaim 2, wherein determining a sensitivity cut-off frequency comprisesmodeling a dispersion curve for a set of borehole parameters.
 4. Themethod of claim 3, wherein the set of borehole parameters is selectedfrom the group consisting of borehole diameter, fluid slowness, density,formation shear slowness, ratio of compressional slowness to shearslowness, and ratio of formation density to fluid density.
 5. The methodof claim 1, wherein generating a set of estimate slowness curves furthercomprises determining the effect of tool presence on the slownesscurves.
 6. The method of claim 5, wherein determining the effect of toolpresence comprises defining an equivalent borehole diameter.
 7. Themethod of claim 6, further comprising scaling the slowness curves by theequivalent borehole diameter.
 8. The method of claim 5, furthercomprising calculating the residual difference R between two dispersioncurves as$R = {\sum\limits_{f}{{{S_{S_{k}}\left( {S,f} \right)}\left\{ {{S_{tool}\left( {S,f,d} \right)} - {S_{empty}\left( {S,f,{d + {a\left( {S,d} \right)}}} \right)}} \right\}}}^{2}}$wherein S is formation shear slowness; S_(Ss), is sensitivity to theformation shear slowness, S_(tool) is a dispersion curve with a toolpresent; S_(empty) is a dispersion curve without the presence of a tool,d is borehole diameter; f is frequency, and a is a constant.
 9. Themethod of claim 8, further comprising minimizing R for a for eachcombination of S and d.
 10. The method of claim 9, further comprisinggenerating a table of offsets (S,d) for more than one dispersion curve.11. The method of claim 1 wherein determining uncertainty in theestimated slowness curves comprises calculating the ratio of sensitivityto borehole diameter to sensitivity to formation shear slowness.
 12. Themethod of claim 1 wherein estimating an uncertainty e in a shearslowness estimate as:${{e\left( {S,f} \right)} = {\frac{s_{hd}\left( {S,f} \right)}{s_{shear}\left( {S,f} \right)}\delta_{hd}}},$wherein S is formation shear slowness; f is frequency, S_(shear) issensitivity to the formation shear slowness, s_(hd) is sensitivity toborehole diameter; and □_(hd) is uncertainty in borehole diametermeasurement.
 13. The method of claim 12, wherein determining an upperlimit for a frequency filter band comprises defining the upper limitwherein E is calculated as E ≥ ∫₀^(f_(u))e(S, f)𝕕f, and wherein E is apredefined threshold.
 14. The method of claim 1, wherein semblance p(S,τ) is computed as:${\rho\left( {S,\tau} \right)} = \frac{\sum\limits_{t = {\tau - T}}^{\tau}{{\sum\limits_{k = 1}^{M}{F^{- 1}\left\{ {{W\left( {f,S,d} \right)}{X_{k}(f)}{\mathbb{e}}^{{- 2}\quad\pi\quad{fir}_{1}{\alpha{({f,S,d})}}}} \right\}}}}^{2}}{\sum\limits_{t = {v - T}}^{T}{\sum\limits_{k = 1}^{M}{{F^{- 1}\left\{ {{W\left( {f,S,d} \right)}{X_{k}(f)}{\mathbb{e}}^{{- 2}\pi\quad{fir}_{1}{\alpha{({f,S,d})}}}} \right\}}}^{2}}}$where xk(t) is the signal of the k^(th) receiver; t is sample time; f isfrequency; F{ } is a Fourier transform; F⁻¹ { } is an inverse Fouriertransform; S is formation shear slowness; d is borehole diameter; τ isthe position of the integration time window, W(f, S, d) is the filterresponse at the cut-off frequencies dynamically computed on theformation shear slowness S; borehole diameter d, a(f, S, d) istheoretical phase delay per unit length at frequency f; i is the squareroot of (−1), r_(k) is the distance between the k^(th) receiver and thestacking reference point; M is the number of receivers; and T is thetime window length in which the semblance is calculated.
 15. A method ofdetermining formation slowness in a borehole comprising: generatingacoustic waves with a transmitter; receiving the acoustic waves using atleast one receiver and generating acoustic raw data; defining a dynamicfrequency filter band; and semblance processing die data using thefrequency filter band.
 16. The method of claim IS, wherein defining adynamic frequency filter band comprises determining the sensitivity ofthe formation slowness to borehole diameter.
 17. The method of claim 15,wherein defining a dynamic frequency filter comprises calculating anequivalent borehole diameter.
 18. The method of claim 15, furthercomprising the step of evaluating a stop criteria and if the stopcriteria is not met, adjusting the filter band and repeating calculationof semblance.
 19. A method of determining processing acoustic datacomprising: (a) generating a set of estimated slowness curves; (b)determining uncertainty in the estimated slowness curves; (c)determining an upper limit for a frequency filter band; (d) determininga lower frequency limit for the frequency filter band; (c) applying thefrequency filter band ill calculating semblance; and (f) repenting steps(a) through (e) across a range of depths in a borehole.
 20. The methodof claim 19, further comprising generating a slowness log from thesemblances.
 21. The method of claim 19, further comprising repeatingsteps (a) through (f) for each receiver in an array.
 22. The method ofclaim 19, farther backpropagating for all slowness curves for eachreceiver in an array.
 23. A method of processing acoustic data collectedusing a borehole tool disposed in a borehole comprising: generating anestimated acoustic response using a tool equivalent model, said toolequivalent model including the effects of the presence of said boreholetool in said borehole; processing said acoustic data at least in partusing the estimated acoustic response such that the processed acousticdata includes the effects of the presence of said borehole tool in saidborehole.
 24. A method according to claim 23 wherein the estimatedacoustic response is set of estimated slowness curves.
 25. A methodaccording to claim 23 wherein said tool model models the borehole toolin the borehole by equivalent coaxial materials.
 26. A method accordingto claim 25 wherein said tool model searches for the various arrivalmodes.
 27. A method according to claim 23 wherein borehole tool iswireline tool.
 28. A method according to claim 24 wherein said step orprocessing comprising the steps of: determining uncertainty in theestimated slowness curves; determining an upper limit for a frequencyfilter band; determining a lower frequency limit for the frequencyfilter band; and applying the frequency filter band in calculatingsemblance.
 29. The method of claim 28, wherein the step of generating aset of curves comprises determining a sensitivity cut-off frequency. 30.The method of claim 29, wherein determining a sensitivity cut-offfrequency comprises modeling a dispersion curve for a set of boreholeparameters.
 31. The method of claim 23, wherein the tool equivalentmodel is based in part on a set of borehole parameters selected from thegroup consisting of borehole diameter, fluid slowness, density,formation shear slowness, ratio of compressional slowness to shearslowness, and ratio of formation density to fluid density.
 32. Themethod of claim 23, wherein the effect of the presence of said boreholetool is determined in part by defining an equivalent borehole diameter.33. The method of claim 24, further comprising scaling the slownesscurves by an equivalent borehole diameter.
 34. The method of claim 24,further comprising calculating the residual difference R between twodispersion curves as$R = {\sum\limits_{f}{{{S_{S_{s}}\left( {S,f} \right)}\left\{ {{S_{tool}\left( {S,f,d} \right)} - {S_{empty}\left( {S,f,{d + {a\left( {S,d} \right)}}} \right)}} \right\}}}^{2}}$wherein S is formation shear slowness; S_(Ss), is sensitivity to theformation shear slowness, S_(tool) is a dispersion curve with a toolpresent; S_(empty) is a dispersion curve without the presence of a tool,d is borehole diameter; f is frequency; and a is a constant.
 35. Themethod of claim 34, further comprising minimizing R for a for eachcombination of S and d.
 36. The method of claim 35, further comprisinggenerating a table of offsets (S,d) for more than one dispersion curve.